The Art of Gymnastics and the Physics of the Double Back Flip
Gymnastics started in ancient Greece around the year 776 b.c. It involves extreme amounts of physical strength, flexibility, agility, coordination, balance, and the ability to rotate your body. It was a performance of combining exercise with amusement and grace. For men's gymnastics there are 6 different events all having their unique set of abilities and skills. The six events include floor, still rings, parallel bars, vault, pommel horse, and the horizontal bar. Although each event has their own very specific sets of skills and the physics behind them, I will only be focusing on the floor routine.
FLOOR
Newton's First Law
Male and female gymnasts both compete on a 12 meter by 12 meter spring floor. The springs in the floor allow gymnasts to manipulate and take advantage of the tension the springs hold in order to achieve their maximum height allowing them to rotate and twist their bodies. Each gymnast is required to have a certain number of tumbling passes, each requiring a certain number of flips and strength skills. Throughout an entire floor routine all of Newton's Laws of Motion can be applied. Newton's First Law, 'An object in motion will remain in motion until an external force is applied,' can be applied to a gymnast doing a round-off (similar to a cartwheel except the gymnast ends by bringing his or her legs together) in order to gain momentum. When a gymnast runs and lunges into a round-off, all of their horizontal momentum is converted into vertical momentum when they soar through the air and it remains until they stop themselves by their feet landing back onto the ground.
Newton's Second Law
Newton's Second Law, 'The acceleration of a body is parallel and directly proportional to the net force and inversely proportional to the mass,' can be applied to a gymnast ability to manipulate the spring floor with speed and weight. The heavier a gymnast is, the more force that is needed to make him or her move. Also the amount of speed that a gymnast uses before flipping will determine how much height they will get. The faster they accelerate the greater amount of force they will exert on the spring floor.
Newton's Third Law
'For every action there is an equal and opposite reaction.' This can be applied to when a gymnast completes a round-off at the beginning of a tumbling pass. The gymnast's body is exerting a force onto the spring floor and the springs in the floor is exerting that same force right back to the gymnasts allowing them to gain sufficient height in order to execute a flip. Sometimes it is difficult for a gymnast to 'stick' a landing because of all the force they apply to the floor on the way down may overwhelm their legs and their balance is disrupted.
The Double Back Flip/Moment of Inertia
The double back flip includes all 3 of Newton's laws of motion and other more specific laws of physics. Applying Newton's laws to this video goes as follows. As the gymnasts starts the routine with the running, he is gaining momentum in order to execute a high enough round off to complete a double back flip. Once the gymnast lunges into the round off, exerting all of his force into the springs of the floor, he gets an equal and opposite force from the springs and launches vertically into the air. As the gymnast comes back down after executing the double back flip he uses his legs and arms to stop his momentum and come to a complete stop. There are other aspects of physics that come into play during the double back flip. A very important aspect of physics that comes into play is moment of inertia. Moment of inertia or 'rotational inertia' refers to an object's resistance to changes during its rotation. Imagine that the gymnast's hips are an axis of rotation. When the arms and legs are closer together to the 'axis' it is easier for the body to rotate. If the gymnast tried to execute this double back flip laid-out (meaning that the body is completely straight with no bending at the hips or knees) he clearly would not make it because there would be too much resistance to rotation with the arms and legs so far away from the 'axis'. The further out the object's mass is, the more rotational inertia the object has, and the more rotational force is required to change its rotation rate. So by tucking (bringing the arms and knees together) he reduces his moment of inertia and rotates faster in order to execute the double back flip. All of these elements put together allows the gymnast to successfully accomplish a double back flip.
The Art of Gymnastics and the Physics of the Double Back Flip
Gymnastics started in ancient Greece around the year 776 b.c. It involves extreme amounts of physical strength, flexibility, agility, coordination, balance, and the ability to rotate your body. It was a performance of combining exercise with amusement and grace. For men's gymnastics there are 6 different events all having their unique set of abilities and skills. The six events include floor, still rings, parallel bars, vault, pommel horse, and the horizontal bar. Although each event has their own very specific sets of skills and the physics behind them, I will only be focusing on the floor routine.
FLOOR
Newton's First Law
Male and female gymnasts both compete on a 12 meter by 12 meter spring floor. The springs in the floor allow gymnasts to manipulate and take advantage of the tension the springs hold in order to achieve their maximum height allowing them to rotate and twist their bodies. Each gymnast is required to have a certain number of tumbling passes, each requiring a certain number of flips and strength skills. Throughout an entire floor routine all of Newton's Laws of Motion can be applied. Newton's First Law, 'An object in motion will remain in motion until an external force is applied,' can be applied to a gymnast doing a round-off (similar to a cartwheel except the gymnast ends by bringing his or her legs together) in order to gain momentum. When a gymnast runs and lunges into a round-off, all of their horizontal momentum is converted into vertical momentum when they soar through the air and it remains until they stop themselves by their feet landing back onto the ground.
Newton's Second Law
Newton's Second Law, 'The acceleration of a body is parallel and directly proportional to the net force and inversely proportional to the mass,' can be applied to a gymnast ability to manipulate the spring floor with speed and weight. The heavier a gymnast is, the more force that is needed to make him or her move. Also the amount of speed that a gymnast uses before flipping will determine how much height they will get. The faster they accelerate the greater amount of force they will exert on the spring floor.
Newton's Third Law
'For every action there is an equal and opposite reaction.' This can be applied to when a gymnast completes a round-off at the beginning of a tumbling pass. The gymnast's body is exerting a force onto the spring floor and the springs in the floor is exerting that same force right back to the gymnasts allowing them to gain sufficient height in order to execute a flip. Sometimes it is difficult for a gymnast to 'stick' a landing because of all the force they apply to the floor on the way down may overwhelm their legs and their balance is disrupted.
The Double Back Flip/Moment of Inertia
The double back flip includes all 3 of Newton's laws of motion and other more specific laws of physics. Applying Newton's laws to this video goes as follows. As the gymnasts starts the routine with the running, he is gaining momentum in order to execute a high enough round off to complete a double back flip. Once the gymnast lunges into the round off, exerting all of his force into the springs of the floor, he gets an equal and opposite force from the springs and launches vertically into the air. As the gymnast comes back down after executing the double back flip he uses his legs and arms to stop his momentum and come to a complete stop. There are other aspects of physics that come into play during the double back flip. A very important aspect of physics that comes into play is moment of inertia. Moment of inertia or 'rotational inertia' refers to an object's resistance to changes during its rotation. Imagine that the gymnast's hips are an axis of rotation. When the arms and legs are closer together to the 'axis' it is easier for the body to rotate. If the gymnast tried to execute this double back flip laid-out (meaning that the body is completely straight with no bending at the hips or knees) he clearly would not make it because there would be too much resistance to rotation with the arms and legs so far away from the 'axis'. The further out the object's mass is, the more rotational inertia the object has, and the more rotational force is required to change its rotation rate. So by tucking (bringing the arms and knees together) he reduces his moment of inertia and rotates faster in order to execute the double back flip. All of these elements put together allows the gymnast to successfully accomplish a double back flip.
Sources
http://www.physicsforums.com/showthread.php?t=252464
http://en.wikipedia.org/wiki/Moment_of_inertia
http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html
http://math2033.uark.edu/wiki/index.php/Gymnastics
http://csep10.phys.utk.edu/astr161/lect/history/newton3laws.html
http://en.wikipedia.org/wiki/Gymnastics